Anisotropy effects on the vibration of circular rings made from crystalline silicon
Anisotropy effects on the vibration of circular rings made from crystalline silicon
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DOI：
10.1006/jsvi.1999.2404
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发表时间：
1999-11-18
影响因子：
4.7
通讯作者：
McWilliam, S
中科院分区：
文献类型：
--
作者：
Eley, R;Fox, CHJ;McWilliam, S
微型工程传感器，如振动陀螺仪、加速计和由晶硅晶片制成的压力传感器，正变得越来越常见。它们通常含有环状部件，其振动特性对换能器的运行至关重要。晶硅材料性质的稳定性对这些器件的性能是非常有利的。然而，材料具有明显的各向异性，在结构设计中必须适当考虑这一点。晶体硅具有三个主平面的立方结构。其中的两个，(111)和(100)面特别令人感兴趣，因为许多器件是由名义上平行于这些面切割的硅晶片制造的。硅相对于主平面的精确切割决定了结构周围材料特性的各向异性的形式和程度。本文着重研究各向异性对晶硅矩形截面圆环固有频率和方向特性的影响。用拉格朗日方程研究了平面内和平面外的弯曲模式。应变能公式中考虑了各向异性的影响。给出了弹性模数方向变化的一般方程。这些方程已被简化和线性化，以允许在一些特殊情况下获得固有频率的解析表达式。给出了由名义上在(100)和(111)主平面上切割的晶片制成的环的结果。研究了从这些主平面切割出的晶片平面内微小偏差的影响。如果环是由各向同性材料制成的，则预测了相似模式对之间的频率分裂，如果环是由各向同性材料制成的，则这些模式将以相同的自然频率简并。用弹性模数的一般表达式和简化表达式得到的频率预测值之间存在差异。这些都是基于对环周围弹性性质变化的傅里叶分析来解释的。(C)1999年学术出版社。
Micro-engineered transducers, such as vibratory gyroscopes, accelerometers and pressure transducers made from wafers of crystalline silicon, are becoming increasingly common. These often contain ring-like components, the vibration properties of which are crucial to the operation of the transducer. The stability of the material properties of crystalline silicon is highly beneficial to the performance of these devices. However, the material has significant anisotropy, which must be properly accounted for in the design of the structure. Crystalline silicon has a cubic structure with three principal planes. Two of these, the (111) and (100) planes, are of particular interest since many devices are manufactured from silicon wafers that are nominally cut parallel to these planes. The precise cut of silicon with respect to the principal planes determines the form and degree of anisotropy in the material properties around a structure. This paper focuses on the effects of anisotropy on the natural frequencies and directional properties of the modes of circular rings of rectangular cross-section, made from crystalline silicon. Both in-plane and out-of-plane flexural modes are investigated using Lagrange's equations. The effects of anisotropy are accounted for in the strain energy formulation. General equations are given for directional variations in the elastic moduli. These equations have been simplified and linearized to allow analytical expressions for the natural frequencies to be obtained for a number of special cases. Results are presented for rings made from wafers that are cut nominally in the (100) and (111) principal planes. The effects of small departures in the plane of the wafer cut from these principal planes is investigated. Frequency splitting is predicted between pairs of similar modes which would be degenerate with equal natural frequencies, if the ring were made from an isotropic material. Differences are found between the frequency predictions obtained using general and simplified expressions for the elasitic moduli. These are explained on the basis of a Fourier analysis of the variation in the elastic properties around the ring. (C) 1999 Academic Press.